The present invention relates to adaptive equalizers for communication receivers of the transversal filter type and particularly to those utilizing fixed increment tap weight adjustments therein.
As is well known in data communication, the channel between the transmitter and the receiver over which data is transmitted not only distorts, but variably distorts, the data transmitted. To overcome the effects of this distortion on the data transmitted at the receiver, i.e to reduce the intersymbol interference which occurs as a result of the distortion, adaptive equalizers have been used. Such adaptive equalizers, also known as adaptive transversal filters or adaptive nonrecursive digital filters, are well-known and often used for this purpose.
Such a known adaptive equalizer is shown in block diagram form in FIG. 1 and may be considered as a sampled analog, i.e. discrete time system or it may be considered a digitized discrete time system with either an infinite number of bits in each digital word or sufficient bits in each digital word such that any quantization errors are entirely negligible. The operation of the system in FIG. 1 is well-known and is set out below to show the general principles of adaptive equalization.
The adaptive equalizer shown in FIG. 1 operates by measuring the intersymbol interference in the output, cross-correlating this intersymbol interference with each tap output and, on the basis of this cross-correlation result, the adaptive equalizer adjusts itself so that the remaining residual intersymbol interference in the output is uncorrelated with any of the tap output signals occurring at nodes, 10, about each of the delay blocks designated 11 in FIG. 1. The delay blocks 11, and nodes 10 viewed as taps, may be considered together as a tapped delay line. As is shown below, when the output error is uncorrelated with any of the tap inputs, the weights of each of the tap output signals are properly adjusted to an optimum for minimizing the intersymbol interference.
X(kT) in FIG. 1 represents a series of data samples each provided in a sample period of time duration T, i.e. a discrete time input signal, which is supplied to the input node of the tapped delay line mentioned above at time t=kT. Again, this tapped delay line comprises the delay blocks 11, also labelled with T's, and the nodes 10 thereabout.
At each node there is provided a tap output signal which is delayed by a number of intervals of duration T equal to the number of delay blocks 11 between that node and the input node at which X(kT) is provided. Each of these tap output signals is supplied to a weighting multiplier, 12, shown as circles also labelled by X, which multiplies the tap output signal by a weighting value, either .omega..sub.1, .omega..sub.2. . . . .omega..sub.N. The delayed tap output signals as so weighted are then summed by a summing means, 13, to provide a discrete time equalizer output signal, Z(kT).
The difference in value between Z(kT) and an estimate of the actual transmitted signal, G(kT), forms an intersymbol interference indication signal or output error, I(kT). The estimate of the actual transmitter signal is determined by a level detector, 14, which has stored in it the allowed amplitudes of the originally transmitted signals and provides as an output, in each sample period, the allowed transmitted signal amplitude level, G(kT), which is most closely approached by Z(kT). The difference between the allowed transmitted level G(kT) and the filtered signal levels experienced at the filter output, Z(kT), is determined by error summer 15. This difference again is taken as a measure of the intersymbol interference and is used to form the signal I(kT).
The intersymbol interference signal I(kT) is then supplied to a set of adjusting multipliers, 16, these again being represented as circles labelled with an X. These adjusting multipliers also receive the corresponding tap output signal which they multiply with I(kT). The multiplication results are integrated by integrators, 17, to average these multiplication results over time, which completes the cross-correlation between I(kT) and X(kT) to provide the weighting values .omega..sub.1, .omega..sub.2. . . , .omega..sub.N. In a discrete time system, the integrators 17 are usually summing devices which provide a running total over time.
The system of FIG. 1 is derived from the following analysis. The adaptive equalizer shown there can be described as a technique to minimize in some sense the intersymbol interference distortion function I(kT). Since events in the adaptive equalization system occur only in sample periods, time is discrete occurring in increments each of duration T to yield an expression for time t=kT with k an integer. The sample periods T are those of the sampled input signal or discrete time input signal, X(kT).
The intersymbol interference distortion signal is the following, as stated above, and as can be seen from FIG. 1: EQU i(kT) = Z(kT) - G(kT).
the sense in which the intersymbol interference is chosen to be minimized is the means square sense which leads to defining the following function to be minimized: ##EQU1## where K is an arbitrary and large number, the number of I.sup.2 (kT) samples to be included in the average.
From FIG. 1, the output of the equalizer at a time t=kT is as follows: ##EQU2## which represents a convolution of the discrete time input signal sequence X(kT) and the adpative equalizer filter characteristic as represented by the sequence of tap output signal weights, .omega..sub.n.
Substituting the intersymbol interference equation into the mean square definition and thereafter substituting the equalizer output function into the result of the first substitution yields the following equation for the mean square function: ##EQU3##
To find the optimum tap weight values .omega..sub.n, this last function must now be minimized with respect to the tap weight values .omega..sub.n which are the independent variables therein. The well-known mathematical step for minimization is to take the N partial derivatives ##EQU4## and then setting these partial derivatives equal to zero. For any particular tap weight, .omega..sub.j, the following is the partial differentiation result for l.ltoreq.j.ltoreq.N: ##EQU5## and which can be placed in the following form: ##EQU6## where, as before, l.ltoreq.j.ltoreq.N. This last equation is obtained from the preceding one through substitution of the third and then the first of the equations set out above. There are N equations just like the equation set out prior to the last equation set out above and each is set to zero to solve for the .omega..sub.n values to provide the optimum adaptive equalizer. These last equations, when implemented, lead to the system shown in FIG. 1, see multipliers 16 and averaging integrators 17.
The adaptive equalizer shown in FIG. 1 and described in the foregoing paragraphs works very well should ideal components be available therefor at economically attractive prices. However, the multipliers available for analog multiplication have unavoidable offsets in them which cause errors in their outputs leading to a degraded performance. Also, the number of such multipliers required for the sampled analog version of the system shown in FIG. 1 can be quite large, easily exceeding 50.
Further, for a number of reasons, it is usually quite attractive to digitize the implementation shown in FIG. 1 and, to hold costs down in such a version, to use as few bits as possible to represent each digital word occurring in the system. This leads to substantial quantization errors which again seriously degrade the performance of the system shown in FIG. 1.